Abstract:

New equilibrium models arising in economy and mechanics will be described by systems of evolutionary generalized equations (EGEs) and thoroughly investigated. Their characteristic feature is the presence of nonsmooth and set-valued mappings. We intend to study various concepts of solutions to systems of such generalized equations and their relevance for particular problems. These EGEs substantially generalize Biot's evolutionary equations which proved to model successfully many problems in physics. Moreover, they can describe evolutionary Stackelberg and/or Nash equilibrium models. This analysis will create a basis for deriving numerical strategies, both for the computation of solutions to these problems as well as to their optimization with respect to design variables or to identification of their parameters via respective inverse problems. The obtained results will be used to numerical solution of applicable model problems.